The correct scholarly view is that if a woman miscarries a foetus that was fully formed, then she should stop praying and fasting because this is postpartum bleeding. If the foetus was not fully formed, then her blood is irregular bleeding and she should not stop praying and fasting.

It is not permissible for a menstruating woman to enter the mosque unless she is only passing through. However, she may sit in a place that is attached to the mosque or close to it and listen to the Khutbah.

If the birth took place without any bleeding, then the woman is not regarded as being in nifas. So, she should fast and pray like all other women who are pure. She should do ghusl so as to be on the safe side.